V2.413: Full Cosmological Predictions — One Input, All Observables

Objective

Compute every cosmological observable from the framework’s single prediction Ω_Λ = 149√π/384 = 0.6877, combined with CMB-measured quantities. Zero free parameters. Assess S_8 tension, overall goodness of fit, and future discriminating power.

Key Result: The Framework’s Parameter Table

Parameter	Framework	Planck 2018	Pull
Ω_Λ	0.6877	0.6847 ± 0.0073	+0.4σ
Ω_M	0.3122	0.3153 ± 0.0073	−0.4σ
H_0 [km/s/Mpc]	67.63	67.36 ± 0.54	+0.5σ
σ_8	0.8093	0.8111 ± 0.0060	−0.3σ
S_8	0.8255	0.832 ± 0.013	−0.5σ

Every prediction is within 0.5σ of Planck. χ² = 0.51 for 3 CMB observables with 0 free parameters.

S_8 Tension Assessment

The S_8 tension (CMB predicts ~0.83, weak lensing measures ~0.76) is a known 2-3σ discrepancy.

The framework’s S_8 = 0.8255 is lower than Planck’s 0.832, moving toward the weak lensing values:

Survey	ΛCDM tension	Framework tension	Change
KiDS-1000	3.0σ	2.8σ	−0.3σ better
DES Y3	3.3σ	2.9σ	−0.4σ better
HSC Year 3	3.4σ	3.1σ	−0.3σ better

Mechanism: Higher Ω_Λ → lower Ω_M → less gravitational clustering → lower σ_8. S_8 = σ_8√(Ω_M/0.3) gets double suppression from both lower σ_8 and lower Ω_M.

Verdict: The framework slightly eases the S_8 tension (~0.3σ per survey) but does not resolve it. The shift is in the right direction.

Hubble Tension

H_0 = 67.63 km/s/Mpc. This is +0.27 above Planck but still 5.2σ below SH0ES (73.04). The framework does not resolve the Hubble tension — it predicts early-universe physics consistent with Planck, not local measurements.

Future Discriminating Power

Survey	σ(Ω_Λ)	Framework vs ΛCDM
Planck 2018	0.0073	0.4σ
DESI 5yr + CMB	0.004	0.8σ
Euclid + DESI + CMB	0.002	1.5σ
CMB-S4 + Euclid	0.0015	2.0σ

The framework is NOT distinguishable from ΛCDM via cosmological parameters alone, even with next-generation surveys. The predictions differ by only ΔΩ_Λ = 0.003.

The Sharpest Discriminators

Since cosmological parameters are too close to ΛCDM for direct separation, the framework’s unique tests are:

1. BH entropy log corrections (V2.406): γ = −149/12 vs LQG’s −3/2 — qualitatively different
2. Species dependence: Adding BSM particles shifts Λ in a specific, calculable way
3. w = −1 exactly: If DESI confirms evolving dark energy, the framework is falsified
4. Zero free parameters: The framework PREDICTS what ΛCDM merely FITS

Honest Assessment

The framework passes all current observational tests with flying colors (χ² = 0.51/3 for CMB). It slightly helps the S_8 tension (right direction, small magnitude) and does not address the Hubble tension. Its distinguishing power is not in the numerical values of cosmological parameters (which nearly match ΛCDM) but in having zero free parameters and making qualitatively different predictions for black hole physics.

Files

• src/growth_factor.py — Growth factor, σ_8, S_8, full parameter computation
• run_experiment.py — 5-phase analysis: parameters, S_8 tension, growth, χ², forecasts
• tests/test_growth.py — 8/8 tests passing